keyFormula
P2310
predicate
Indicates that a formula serves as the primary or defining expression associated with an entity or relationship.
All labels observed (35)
| Label | Occurrences |
|---|---|
| mathematicalForm | 239 |
| hasFormula | 74 |
| formula | 24 |
| openingFormula | 15 |
| hasKeyFormula | 14 |
| containsFormula | 10 |
| coreFormula | 7 |
| satisfiesEquation | 7 |
| coreEquation | 6 |
| keyFormula canonical | 4 |
| mathematicalExpression | 4 |
| costSharingFormula | 3 |
| definitionFormula | 3 |
| famousFormula | 3 |
| keyFormulaOfCategoricalImperative | 3 |
| typicalFormula | 3 |
| centralFormula | 2 |
| standardFormula | 2 |
| GOEFormula | 1 |
| GUEFormula | 1 |
| bracketFormula | 1 |
| codeRateFormula | 1 |
| combinedFormula | 1 |
| commonFormula | 1 |
| definedByFormula | 1 |
| establishedFormula | 1 |
| formulaInFrequencyForm | 1 |
| hasEntropyFormula | 1 |
| hasFormulaForShift | 1 |
| kernelFormula | 1 |
| keyStatementFormula | 1 |
| mainFormula | 1 |
| originalFormulaFor | 1 |
| primeFormula | 1 |
| usesSchedulingFormula | 1 |
Description generation (PDg)
The one-sentence description above was generated by prompting gpt-5.1 with the predicate name and this instruction.
Instruction
Given a predicate that represents a relationship or action between entities, generate a one-sentence description explaining its meaning. # Instructions Focus on describing the relationship, not the entities themselves. # Response Format Begin the description with \' Indicates...\'
Input
Predicate: keyFormula
Generated description
Indicates that a formula serves as the primary or defining expression associated with an entity or relationship.
Sample triples (440)
| Subject | Object |
|---|---|
| Bloch equations | first-order linear differential equations via predicate surface "mathematicalForm" ⓘ |
| Nyquist theorem | fs > 2B, where fs is sampling frequency and B is highest signal frequency via predicate surface "mathematicalForm" ⓘ |
| Newcomb tables of the Sun, Mercury, Venus, and Mars | series expansions in time via predicate surface "mathematicalForm" ⓘ |
| Vandermonde's identity | For integers m,n,r: sum_{k} C(m,k) C(n,r-k) = C(m+n,r) via predicate surface "hasFormula" ⓘ |
| Vandermonde's identity | \(\sum_{k=0}^{r} \binom{m}{k}\binom{n}{r-k} = \binom{m+n}{r}\) via predicate surface "hasFormula" ⓘ |
| Vandermonde's identity | \(\sum_{k} \binom{m}{k}\binom{n}{r-k} = 0\) if r<0 or r>m+n via predicate surface "hasFormula" ⓘ |
| Planck–Einstein relation | E = hν via predicate surface "hasFormula" ⓘ |
| Onsager reciprocal relations | J_i = Σ_j L_ij X_j via predicate surface "mathematicalForm" ⓘ |
| Onsager–Machlup function | time integral of a Lagrangian-like density along a path via predicate surface "mathematicalForm" ⓘ |
| Cottrell equation | i(t) = n F A C \sqrt{D / (\pi t)} via predicate surface "mathematicalForm" ⓘ |
| law of conservation of mass | sum of masses before equals sum of masses after via predicate surface "mathematicalForm" ⓘ |
| Doppler effect | f′ = f (c ± v_o) / (c ∓ v_s) via predicate surface "mathematicalForm" ⓘ |
| Gell-Mann–Okubo mass formula | linear relation among hadron masses in a multiplet via predicate surface "mathematicalForm" ⓘ |
| Kolmogorov distance | d_K(F,G) = sup_x |F(x) − G(x)| via predicate surface "mathematicalForm" ⓘ |
| Jacobi integral | sum of kinetic energy term and effective potential term in rotating frame via predicate surface "mathematicalForm" ⓘ |
| Lagrangian-history closure approximation | integro-differential equations for correlation functions via predicate surface "mathematicalForm" ⓘ |
| Kraichnan model of passive scalar advection | advection-diffusion equation with random velocity field via predicate surface "coreEquation" ⓘ |
| third law of thermodynamics | S → 0 as T → 0 for a perfect crystal via predicate surface "mathematicalForm" ⓘ |
| Esaki–Tsu relation | drift velocity proportional to (ω_B τ)/(1 + (ω_B τ)^2) via predicate surface "mathematicalForm" ⓘ |
| Droop quota | floor( validVotes / (seats + 1) ) + 1 via predicate surface "hasFormula" ⓘ |
| the examined life | related to the claim "the unexamined life is not worth living" via predicate surface "famousFormula" ⓘ |
| Kalman filter | recursive algorithm via predicate surface "mathematicalForm" ⓘ |
| Hicksian demand | function h(p,u) mapping prices and utility to demanded bundles via predicate surface "mathematicalForm" ⓘ |
| Kaldor–Verdoorn law | labor productivity growth is a linear function of output growth via predicate surface "mathematicalForm" ⓘ |
| Fisher's linear discriminant | generalized eigenvalue problem via predicate surface "mathematicalForm" ⓘ |
| Larmor precession | ω = γ B via predicate surface "hasFormula" ⓘ |
| Larmor precession | ω = −γ B for sign convention including gyromagnetic ratio sign via predicate surface "hasFormula" ⓘ |
| Landé g-factor | g_J = 1 + [j(j+1) + s(s+1) - l(l+1)] / [2 j(j+1)] via predicate surface "hasFormula" ⓘ |
| Kobayashi–Maskawa theory | 3×3 unitary matrix via predicate surface "mathematicalForm" ⓘ |
| Sommerfeld expansion in statistical mechanics | integral expressed as series involving derivatives of g(ε) at ε = μ via predicate surface "mathematicalForm" ⓘ |
| Sommerfeld radiation condition | lim_{r→∞} r^{(d-1)/2}(∂u/∂r - iku) = 0 for d-dimensional space via predicate surface "mathematicalForm" ⓘ |
| Sommerfeld radiation condition | lim_{r→∞} r(∂u/∂r - iku) = 0 in three dimensions via predicate surface "mathematicalForm" ⓘ |
|
Vlasov equation (for long-range interactions and negligible collisions)
surface form:
Vlasov equation
|
first-order partial differential equation in time via predicate surface "mathematicalForm" ⓘ |
|
Vlasov equation (for long-range interactions and negligible collisions)
surface form:
Vlasov equation
|
first-order partial differential equation in phase-space coordinates via predicate surface "mathematicalForm" ⓘ |
| Pauli–Villars regularization | replacement of bare propagator by sum over regulator propagators via predicate surface "mathematicalForm" ⓘ |
| Einasto density profile | exponential of a power of radius via predicate surface "mathematicalForm" ⓘ |
| Cauchy residue theorem | ∮_γ f(z) dz = 2πi Σ Res(f, a_k) for singularities a_k inside γ via predicate surface "formula" ⓘ |
| Hotelling’s lemma | profit function is convex in prices under standard assumptions via predicate surface "mathematicalForm" ⓘ |
| Chernoff information | defined as the negative logarithm of the minimum Chernoff moment over s in [0,1] via predicate surface "mathematicalForm" ⓘ |
| Tsallis divergence | q-deformed divergence via predicate surface "mathematicalForm" ⓘ |
| Cauchy integral formula | f(z0) = (1/(2πi)) ∮_Γ f(z)/(z−z0) dz via predicate surface "mathematicalExpression" ⓘ |
| Lusser's law | R_system = Π R_i via predicate surface "mathematicalForm" ⓘ |
| Lusser's law of series system reliability | R_system = ∏ R_i via predicate surface "hasFormula" ⓘ |
| Lusser's law of series system reliability | R_system = R_1 × R_2 × … × R_n via predicate surface "hasFormula" ⓘ |
| Pratikraman | Micchami Dukkadam via predicate surface "coreFormula" ⓘ |
| Salpeter initial mass function | ξ(M) ∝ M^{-α} via predicate surface "mathematicalForm" ⓘ |
| Simpson's rule | ∫_a^b f(x) dx ≈ (h/3)[f(x₀)+4f(x₁)+2f(x₂)+4f(x₃)+…+4f(x_{n−1})+f(x_n)] via predicate surface "formula" ⓘ |
| Hebbian learning | Δw ∝ x·y via predicate surface "mathematicalForm" ⓘ |
| Shields parameter | θ = τ / [(ρ_s − ρ) g d] via predicate surface "hasFormula" ⓘ |
| Institution Narrative | “This is my body” via predicate surface "containsFormula" ⓘ |